Study of the $\Lambda \to p\ell {\bar{\nu }}_{\ell }$ semileptonic decay in lattice QCD

Abstract

We present the first lattice QCD determination of the $\Lambda \to N$ vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay $\Lambda \to p\ell {\bar{\nu }}_{\ell }$. This channel provides a clean, theoretically controlled avenue for extracting the CKM matrix element $|V_{us}|$ from the baryon sector. Our analysis uses a gauge ensemble with physical light, strange, and charm quark masses and yields the most precise determination to date of the full set of transition form factors -- including second-class contributions -- as well as the associated couplings, radii, and the ratio of muon-to-electron decay rates, an observable sensitive to possible non-standard scalar and tensor interactions. We compare our non-perturbative results with next-to-next-to-leading order expansions in the small parameter $\delta =(m_{\Lambda }-m_N)/m_{\Lambda }\approx 0.16$. We find that the common phenomenological approximation of neglecting the $q^2$-dependence of the form factors leads to a $\sim 4\%$ deviation in the decay rate. This underscores the critical importance of precise, fully non-perturbative form factor inputs for achieving the sub-percent precision targets of upcoming experimental programs.

Comments: Updated version, 5 pages + supplementary material, 8 figures. Erratum for v1 and v2: The overall sign in Eq.(57) was incorrect, affecting the resulting F3 form factor. This is now corrected